My copending application Ser. No. 07/200,431 filed on May 31, 1988, discloses a picket fence construction wherein top and bottom horizontal rails are provided with triangular openings into which the end portions of complimentary triangular pickets are inserted. The pickets are provided with indentations at the locations of the rails to permit rotation of the pickets into locking engagement with the rails. Decorative caps are slidably mounted on the pickets and include fingers which depend into the respective openings in the rails adjacent the pickets to prevent spurious rotation of the pickets and subsequent disassembly of the fence. In those applications where the picket fence is used for purposes of security it is important to prevent the surreptitious disassembly of the pickets.